The (E + A) x (e + a) Jahn-Teller and pseudo-Jahn-Teller Hamiltonian including spin-orbit coupling for trigonal systems

The Hamiltonian describing E x e Jahn-Teller (JT) coupling and (E + A) x (e + a) pseudo-JT (PJT) coupling is developed beyond the standard JT theory for the example of XY3 systems, taking the bending modes of a and e symmetry into account. For the electrostatic (spin-free) Hamiltonian, the conventional Taylor expansion up to second order in symmetry-adapted displacements is replaced by an expansion in invariant polynomials up to arbitrarily high orders. The relevance of a systematic high-order expansion in the three large-amplitude bending modes is illustrated by the construction of an eighth-order threesheeted three-dimensional ab initio potential-energy surface for PH₃⁺. The theory of spin-orbit coupling in trigonal JT/PJT systems is extended beyond the standard model of JT theory by an expansion of the microscopic Breit-Pauli operator up to second order in symmetry-adapted vibrational coordinates. It is shown that a linear E x e JT effect of relativistic origin exists in C_3v systems which vanishes at the planar (D_3h) geometry. The linear relativistic ²E - ²A PJT coupling, on the other hand, persists at the planar geometry.(Graph Presented).